Tuesday, March 18, 2014

Bracket Math for the MDS Model

I finally finished my own MDS Model for college basketball, and got it done just in time to predict the bracket. Since it wasn't in action for any of the regular season, I have no baseline to measure its performance against. Here goes nothing!


Here's the predicted bracket (based on my Pyth rating):



Not many major differences, and we end up with the same Final Four. All the ratings love Louisville though. Here are the full round-by-round probabilities:

SeedTeam1st Round2nd RoundSweet 16Elite 8Final FourChampionshipChampion
1Florida100.00%98.49%75.34%51.40%31.58%20.52%9.89%
16*Albany56.41%0.95%0.06%0.00%0.00%0.00%0.00%
16*Mount St. Mary's43.59%0.57%0.03%0.00%0.00%0.00%0.00%
8Colorado100.00%28.06%3.96%1.01%0.21%0.05%0.01%
9Pittsburgh100.00%71.94%20.61%9.41%3.66%1.54%0.42%
5VCU100.00%86.12%45.85%17.84%7.87%3.73%1.19%
12Stephen F. Austin100.00%13.88%2.40%0.25%0.03%0.00%0.00%
4UCLA100.00%79.44%45.91%19.11%8.97%4.51%1.55%
13Tulsa100.00%20.56%5.84%0.98%0.19%0.04%0.01%
6Ohio St.100.00%76.35%54.16%27.53%13.47%7.42%2.86%
11Dayton100.00%23.65%10.58%2.74%0.65%0.18%0.03%
3Syracuse100.00%84.38%33.42%11.64%3.81%1.45%0.35%
14Western Michigan100.00%15.62%1.83%0.18%0.02%0.00%0.00%
7New Mexico100.00%54.64%14.18%5.39%1.54%0.52%0.11%
10Stanford100.00%45.36%10.35%3.51%0.88%0.26%0.05%
2Kansas100.00%96.10%74.98%48.96%27.12%16.67%7.45%
15Eastern Kentucky100.00%3.90%0.49%0.04%0.00%0.00%0.00%
1Virginia100.00%97.92%76.23%46.15%27.77%13.68%5.45%
16Coastal Carolina100.00%2.08%0.15%0.01%0.00%0.00%0.00%
8Memphis100.00%55.72%14.12%4.72%1.56%0.38%0.07%
9George Washington100.00%44.28%9.50%2.73%0.77%0.16%0.02%
5Cincinnati100.00%59.78%24.24%9.72%4.18%1.37%0.35%
12Harvard100.00%40.22%12.95%4.10%1.40%0.35%0.07%
4Michigan St.100.00%92.54%61.75%32.49%18.23%8.23%2.97%
13Delaware100.00%7.46%1.06%0.10%0.01%0.00%0.00%
6North Carolina100.00%70.47%34.24%13.84%5.31%1.70%0.42%
11Providence100.00%29.53%8.84%2.02%0.43%0.07%0.01%
3Iowa St.100.00%89.84%55.26%25.35%11.10%4.12%1.19%
14North Carolina Central100.00%10.16%1.66%0.16%0.01%0.00%0.00%
7Connecticut100.00%64.95%22.35%10.69%3.96%1.22%0.29%
10Saint Joseph's100.00%35.05%7.99%2.68%0.66%0.13%0.02%
2Villanova100.00%96.73%69.39%45.24%24.62%11.69%4.46%
15Milwaukee100.00%3.27%0.27%0.02%0.00%0.00%0.00%
1Arizona100.00%98.46%77.46%67.36%51.39%33.19%23.63%
16Weber St.100.00%1.54%0.09%0.01%0.00%0.00%0.00%
8Gonzaga100.00%42.00%8.15%4.93%2.11%0.66%0.24%
9Oklahoma St.100.00%58.00%14.30%9.68%4.89%1.86%0.82%
5Oklahoma100.00%69.94%39.35%7.86%2.87%0.75%0.23%
12North Dakota St.100.00%30.06%11.04%1.12%0.23%0.03%0.01%
4San Diego St.100.00%76.51%42.81%8.54%3.12%0.81%0.25%
13New Mexico St.100.00%23.49%6.80%0.51%0.08%0.01%0.00%
6Baylor100.00%68.17%24.12%9.64%2.43%0.64%0.20%
11Nebraska100.00%31.83%6.90%1.68%0.25%0.04%0.01%
3Creighton100.00%92.68%67.62%39.55%15.75%6.73%3.31%
14Louisiana Lafayette100.00%7.32%1.36%0.15%0.01%0.00%0.00%
7Oregon100.00%59.36%23.62%9.90%2.70%0.78%0.26%
10BYU100.00%40.64%12.95%4.36%0.92%0.20%0.05%
2Wisconsin100.00%92.26%62.27%34.59%13.24%5.43%2.57%
15American100.00%7.74%1.17%0.13%0.01%0.00%0.00%
1Wichita St.100.00%96.64%55.11%19.87%10.89%4.42%2.12%
16*Cal Poly77.11%3.08%0.18%0.01%0.00%0.00%0.00%
16*Texas Southern22.89%0.28%0.01%0.00%0.00%0.00%0.00%
8Kentucky100.00%73.31%37.19%13.16%7.11%2.83%1.33%
9Kansas St.100.00%26.69%7.52%1.41%0.43%0.09%0.02%
5Saint Louis100.00%67.32%12.29%4.09%1.47%0.37%0.11%
12*North Carolina St.37.93%9.92%0.83%0.13%0.02%0.00%0.00%
12*Xavier62.07%22.77%2.78%0.63%0.16%0.03%0.01%
4Louisville100.00%94.72%82.58%60.51%45.33%27.80%19.32%
13Manhattan100.00%5.28%1.52%0.21%0.03%0.00%0.00%
6Massachusetts100.00%33.02%9.13%3.56%0.68%0.14%0.04%
11*Iowa51.23%34.59%14.70%8.26%2.62%0.89%0.36%
11*Tennessee48.77%32.39%13.41%7.38%2.27%0.75%0.29%
3Duke100.00%89.36%60.54%40.91%17.43%7.80%4.09%
14Mercer100.00%10.64%2.22%0.48%0.04%0.00%0.00%
7Texas100.00%46.04%13.21%3.18%0.49%0.08%0.02%
10Arizona St.100.00%53.96%17.17%4.62%0.81%0.16%0.04%
2Michigan100.00%96.43%69.31%31.60%10.19%3.51%1.44%
15Wofford100.00%3.57%0.31%0.01%0.00%0.00%0.00%

And here are the final ratings as well, for all 351 teams:

RankTeamRate
1Arizona0.976
2Louisville0.974
3Florida0.960
4Kansas0.953
5Duke0.946
6Virginia0.943
7Ohio St.0.940
8Creighton0.939
9Villanova0.938
10Wichita St.0.936
11Wisconsin0.934
12Kentucky0.933
13Michigan St.0.933
14UCLA0.927
15Oklahoma St.0.925
16VCU0.919
17Michigan0.916
18Iowa0.914
19Tennessee0.910
20Iowa St.0.907
21Pittsburgh0.901
22Gonzaga0.900
23Cincinnati0.889
24Oregon0.888
25North Carolina0.886
26Syracuse0.884
27Connecticut0.880
28Baylor0.875
29Oklahoma0.872
30San Diego St.0.872
31Saint Louis0.867
32New Mexico0.862
33Arkansas0.846
34BYU0.845
35Harvard0.844
36Stanford0.838
37Memphis0.838
38Kansas St.0.836
39Massachusetts0.836
40Minnesota0.831
41St. John's0.831
42Dayton0.828
43Louisiana Tech0.826
44Southern Methodist0.825
45Georgetown0.820
46Arizona St.0.820
47Florida State0.805
48George Washington0.804
49Saint Joseph's0.798
50Texas0.796
51Maryland0.794
52Saint Mary's0.791
53Xavier0.791
54Clemson0.789
55Indiana0.789
56Utah0.786
57West Virginia0.782
58Colorado0.779
59LSU0.774
60Tulsa0.768
61Nebraska0.766
62Providence0.764
63Boise State0.760
64Alabama0.754
65Missouri0.754
66California0.750
67Illinois0.749
68North Dakota St.0.746
69Southern Miss0.741
70Green Bay0.725
71Georgia0.721
72Marquette0.712
73St. Bonaventure0.710
74UNLV0.702
75North Carolina St.0.698
76Richmond0.696
77Penn State0.695
78La Salle0.695
79Ole Miss0.686
80Northern Iowa0.682
81San Francisco0.680
82Iona0.680
83Middle Tennessee0.677
84New Mexico St.0.677
85Mercer0.676
86Miami (FL)0.676
87Notre Dame0.676
88Manhattan0.673
89Georgia State0.671
90Texas Tech0.670
91Seton Hall0.665
92UTEP0.662
93Ohio0.658
94Vermont0.656
95Stephen F. Austin0.646
96Oregon State0.641
97Buffalo0.638
98Purdue0.634
99Cleveland State0.634
100Washington0.618
101Eastern Michigan0.617
102Wyoming0.617
103Columbia0.616
104George Mason0.613
105Toledo0.610
106Vanderbilt0.606
107Butler0.601
108Texas A&M0.595
109Belmont0.593
110South Carolina0.591
111Western Michigan0.585
112Portland0.583
113UC Irvine0.581
114UC Santa Barbara0.581
115Boston University0.576
116Princeton0.565
117Temple0.559
118Rhode Island0.558
119Indiana State0.558
120Utah State0.551
121Fresno State0.549
122Louisiana Lafayette0.547
123Denver0.545
124American0.544
125Wake Forest0.540
126Akron0.537
127Auburn0.537
128Colorado State0.535
129UAB0.528
130Delaware0.527
131North Carolina Central0.525
132Hawaii0.525
133Nevada0.523
134Canisius0.516
135Drexel0.511
136San Diego0.502
137Illinois State0.500
138USC0.492
139Pacific0.490
140Missouri State0.485
141Davidson0.483
142Boston College0.481
143Northwestern0.467
144Georgia Tech0.459
145Quinnipiac0.454
146Eastern Kentucky0.453
147Southern Illinois0.444
148Towson0.443
149Bucknell0.441
150DePaul0.440
151Northeastern0.432
152Pepperdine0.431
153Virginia Tech0.428
154Bowling Green0.427
155Charlotte0.425
156Santa Clara0.422
157South Dakota State0.416
158Oakland0.408
159Rutgers0.407
160Loyola Marymount0.407
161William & Mary0.402
162Wright State0.402
163Holy Cross0.401
164Long Beach State0.399
165Drake0.398
166Valparaiso0.391
167Duquesne0.386
168Weber St.0.385
169Houston0.383
170Yale0.382
171Florida Gulf Coast0.381
172Murray State0.381
173Morehead State0.380
174USC Upstate0.379
175Kent State0.378
176Cal Poly0.376
177Washington State0.372
178Old Dominion0.372
179Siena0.370
180Colgate0.370
181Charleston0.368
182UCF0.367
183Oral Roberts0.365
184Western Kentucky0.364
185Brown0.354
186IPFW0.349
187Milwaukee0.340
188Elon0.339
189Detroit0.333
190Youngstown State0.332
191Southern University0.331
192East Carolina0.330
193Miami (OH)0.327
194Fordham0.322
195Arkansas State0.321
196North Texas0.319
197Evansville0.318
198Stony Brook0.316
199Northwestern State0.316
200Rider0.314
201Nebraska-Omaha0.313
202Bryant University0.306
203Montana0.303
204Niagara0.297
205Bradley0.297
206Northern Illinois0.294
207Marist0.294
208Marshall0.293
209Charleston Southern0.292
210Mississippi State0.289
211Albany0.288
212Robert Morris0.288
213Wofford0.287
214Florida Atlantic0.282
215Texas-Arlington0.281
216Loyola (IL)0.281
217East Tennessee State0.276
218Sam Houston State0.272
219Arkansas-Little Rock0.272
220Dartmouth0.270
221Lafayette0.265
222TCU0.264
223South Florida0.264
224St. Francis (NY)0.263
225Coastal Carolina0.259
226Hofstra0.259
227Seattle0.257
228North Dakota0.257
229Northern Colorado0.255
230UNC Asheville0.254
231Eastern Washington0.253
232Louisiana-Monroe0.253
233Cal State Bakersfield0.252
234South Alabama0.251
235Wagner0.250
236Idaho State0.249
237Troy0.248
238Air Force0.245
239Utah Valley0.244
240Fairfield0.243
241Mount St. Mary's0.238
242Lehigh0.235
243Idaho0.235
244Winthrop0.234
245St. Peter's0.232
246Hampton0.231
247Morgan State0.230
248James Madison0.229
249Tennessee State0.225
250Army0.224
251South Dakota0.220
252Illinois-Chicago0.217
253Florida International0.216
254Grand Canyon0.209
255Texas A&M-CC0.207
256Monmouth0.202
257North Florida0.202
258Ball State0.200
259Western Illinois0.198
260High Point0.196
261Cal State Fullerton0.195
262Western Carolina0.195
263Texas State0.194
264Cal State Northridge0.193
265Northern Arizona0.189
266Central Michigan0.186
267Pennsylvania0.186
268Tennessee Tech0.184
269UMKC0.182
270Lipscomb0.176
271Liberty0.174
272Virginia Military0.172
273Portland State0.167
274North Carolina-Wilmington0.165
275Norfolk State0.161
276Gardner-Webb0.157
277Southeast Missouri State0.156
278Hartford0.155
279Sacramento State0.155
280Tulane0.152
281Texas Southern0.152
282San Jose State0.149
283Incarnate Word0.144
284Northern Kentucky0.138
285Rice0.138
286UTSA0.136
287Coppin State0.135
288Texas-Pan American0.133
289Chicago State0.129
290Austin Peay0.126
291Fairleigh Dickinson0.125
292UC Riverside0.123
293Jackson State0.120
294Jacksonville0.118
295Loyola (MD)0.114
296IUPUI0.112
297SIU-Edwardsville0.112
298Sacred Heart0.110
299Montana State0.105
300Chattanooga0.102
301LIU Brooklyn0.101
302Radford0.098
303Jacksonville State0.097
304Eastern Illinois0.094
305Central Connecticut State0.094
306Cornell0.092
307Savannah State0.092
308McNeese State0.088
309Georgia Southern0.085
310Alabama A&M0.083
311Alabama State0.083
312Kennesaw State0.083
313UC Davis0.079
314UNC Greensboro0.077
315Tennessee-Martin0.077
316Southeastern Louisiana0.077
317Navy0.077
318St. Francis U0.075
319Appalachian State0.074
320Lamar0.073
321Samford0.072
322Florida A&M0.072
323Campbell0.068
324Maine0.067
325New Hampshire0.067
326N.J.I.T.0.067
327Prairie View A&M0.066
328New Orleans0.065
329Arkansas-Pine Bluff0.064
330UMBC0.064
331Nicholls State0.064
332Massachusetts Lowell0.063
333Delaware State0.061
334Alcorn State0.059
335Stetson0.056
336Central Arkansas0.056
337Citadel0.047
338Houston Baptist0.046
339Binghamton0.045
340North Carolina A&T0.040
341Howard0.039
342Maryland-Eastern Shore0.037
343South Carolina State0.035
344Bethune-Cookman0.035
345Southern Utah0.033
346Longwood0.032
347Abilene Christian0.029
348Mississippi Valley State0.027
349Furman0.026
350Presbyterian0.024
351Grambling State0.019

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